Question

In a duct in which air is flowing, a normal shock wave occurs at a Mach number of 1.5. The static pressure and temperature upstream of the shock wave are 170 kN/m2 and 23°C respectively. Determine : 

(i) Pressure, temperature and Mach number downstream of the shock, and 

(ii) Strength of shock. Take γ = 1.4.

Answer 1

Let subscripts 1 and 2 represent flow conditions upstream and downstream of the shock wave respectively. 

Mach number, M₁ = 1.5 

Upstream pressure, p₁ = 170 kN/m² 

Upstream temperature, T₁ = 23 + 273 = 296 K 

γ = 1.4 

(i) Pressure, temperature and Mach number downstream of the shock :

M₂ = 0.7.

(ii) Strength of shock : 

Strength of shock = p₂/p₁ – 1 = 2.458 – 1 = 1.458.